1{
  2  "device_available": "cuda",
  3  "finite_difference": {
  4    "autograd_residual": 2.0,
  5    "finite_difference_residual": 2.000000000002,
  6    "absolute_error": 2.000177801164682e-12
  7  },
  8  "lambda_sweep": [
  9    {
 10      "lambda": 0.0,
 11      "a_b": [
 12        0.9999999986334784,
 13        -0.9999999986334784
 14      ],
 15      "observed_abs_residual": 1.9999999972669569,
 16      "predicted_abs_residual": 2.0,
 17      "fit_loss": 1.867381180978464e-18,
 18      "relative_error": 1.3665215625728695e-09
 19    },
 20    {
 21      "lambda": 0.05,
 22      "a_b": [
 23        0.8333333333159836,
 24        -0.8333333333159836
 25      ],
 26      "observed_abs_residual": 1.6666666666319672,
 27      "predicted_abs_residual": 1.6666666666666667,
 28      "fit_loss": 0.02777777778356103,
 29      "relative_error": 2.0819745927257156e-11
 30    },
 31    {
 32      "lambda": 0.25,
 33      "a_b": [
 34        0.49999999999999967,
 35        -0.49999999999999967
 36      ],
 37      "observed_abs_residual": 0.9999999999999993,
 38      "predicted_abs_residual": 1.0,
 39      "fit_loss": 0.25000000000000033,
 40      "relative_error": 6.661338147744277e-16
 41    },
 42    {
 43      "lambda": 0.5,
 44      "a_b": [
 45        0.33333333333333315,
 46        -0.33333333333333315
 47      ],
 48      "observed_abs_residual": 0.6666666666666663,
 49      "predicted_abs_residual": 0.6666666666666666,
 50      "fit_loss": 0.4444444444444447,
 51      "relative_error": 4.996003610805711e-16
 52    },
 53    {
 54      "lambda": 1.0,
 55      "a_b": [
 56        0.19999999999999993,
 57        -0.19999999999999993
 58      ],
 59      "observed_abs_residual": 0.39999999999999986,
 60      "predicted_abs_residual": 0.4,
 61      "fit_loss": 0.6400000000000001,
 62      "relative_error": 4.1633363423339285e-16
 63    },
 64    {
 65      "lambda": 2.0,
 66      "a_b": [
 67        0.1111111111111111,
 68        -0.1111111111111111
 69      ],
 70      "observed_abs_residual": 0.2222222222222222,
 71      "predicted_abs_residual": 0.2222222222222222,
 72      "fit_loss": 0.7901234567901234,
 73      "relative_error": 0.0
 74    },
 75    {
 76      "lambda": 5.0,
 77      "a_b": [
 78        0.047619047619047616,
 79        -0.047619047619047616
 80      ],
 81      "observed_abs_residual": 0.09523809523809523,
 82      "predicted_abs_residual": 0.09523809523809523,
 83      "fit_loss": 0.9070294784580498,
 84      "relative_error": 0.0
 85    }
 86  ],
 87  "gamma_sweep": [
 88    {
 89      "gamma": 0.25,
 90      "observed": 64.0,
 91      "predicted": 64.0,
 92      "relative_error": 0.0
 93    },
 94    {
 95      "gamma": 0.5,
 96      "observed": 16.0,
 97      "predicted": 16.0,
 98      "relative_error": 0.0
 99    },
100    {
101      "gamma": 1.0,
102      "observed": 4.0,
103      "predicted": 4.0,
104      "relative_error": 0.0
105    },
106    {
107      "gamma": 2.0,
108      "observed": 1.0,
109      "predicted": 1.0,
110      "relative_error": 0.0
111    },
112    {
113      "gamma": 4.0,
114      "observed": 0.25,
115      "predicted": 0.25,
116      "relative_error": 0.0
117    }
118  ],
119  "mini_compare": [
120    {
121      "method": "baseline",
122      "lambda": 0.0,
123      "final_abs_cross_partial": 1.9999999972669569,
124      "critic_fit_loss": 1.867381180978464e-18,
125      "coefficients": [
126        0.9999999986334784,
127        -0.9999999986334784
128      ]
129    },
130    {
131      "method": "compat_regularized",
132      "lambda": 1.0,
133      "final_abs_cross_partial": 0.39999999999999986,
134      "critic_fit_loss": 0.6400000000000001,
135      "coefficients": [
136        0.19999999999999993,
137        -0.19999999999999993
138      ]
139    }
140  ],
141  "predictions": [
142    "At lambda=0 residual=2; increasing lambda follows 2/(1+4 lambda).",
143    "The Gibbs incompatibility squared scales as 1/gamma^2, so halving gamma quadruples it.",
144    "At large lambda residual tends to zero (compatibility), while fitting error increases because targets are intentionally incompatible."
145  ]
146}